Monday, June 05, 2006

June 2006: Shaking hands (solution)

This is the solution to the Shaking Hands puzzle.

Mr. Dickinson shook hands with 4 people.

Suppose the other four couples are Mr. and Mrs. A, Mr. and Mrs. B, Mr. and Mrs. C, and Mr. and Mrs. D. We know Mr. Dickinson did not shake hands with 8 people, because if he did, then everyone else would have shaken hands with at least one person, and we know that someone shook zero hands. Say that it was Mr. A who shook 8 hands. Then Mrs. A must have shaken 0 (in the graph below, lines indicate hand shakes). By a similar logic, Mr. Dickinson couldn't have shaken 7 hands, because then no one could have shaken 1 hand. Say Mr. B shook 7 hands. Then Mrs. B shook 1 hand. Arguing in the same way, Mr. Dickinson couldn't have shaken 6 hands, so someone else did---Mr. C, say. Then Mrs. C shook 2 hands. And again, someone else shook 5 hands, Mr. D, and his wife, Mrs. D, shook 3 hands. Thus, Mr. Dickinson shook 4 hands.

This month's winners: Evan Templeton, Ryan Deeds, Jared Lease, Shashwat Acharya, Hiro Arai

June 2006: Shaking hands

Mr. and Mrs. Dickinson invited four couples to their house for a dinner party. Some of the guests knew each other, and others did not. Those who did not know each other shook hands upon meeting. Mrs. Dickinson happened to notice something curious: each person (not including herself) shook hands with a different number of people (one person shook no hands, one person shook one hand, one person shook two hands, etc.). How many hands did Mr. Dickinson shake?

Hint: Mr. Dickinson did not shake eight hands, for if he did, then no one could have shaken zero hands.

Dickinson College students can submit their answers to Dave Richeson. The list of solvers will be posted at the end of June.

From: "Effective Problem Solving, 2nd Edition," Marvin Levine, Prentice-Hall, 1994

May 2006: Tait's 8 Coin Puzzle (solution)

This is the solution to Tait's 8 Coin Puzzle:

This month's winners are: Evan Templeton, Jon Rogers, Jared Lease, Gordon Clark, Shashwat Acharya